A tripling construction for overlarge sets of KTS

作者：Yuan Landang^*; Kang Qingde

来源：Discrete Mathematics, 2009, 309(4): 975-981.

DOI：10.1016/j.disc.2008.01.001

• Kirkman triple system
• Generalized frame
• Overlarge set
• (2,1)-resolvable Steiner quadruple system

An overlargeset of KTS(v), denoted by OLKTS(v), is a collection {(X \ {x}, B(x)) : x is an element of X}, where X is a (v 1)-set, each (X \ {x}, B(x)) is a KTS(v) and {B(x) : x is an element of X} forms a partition of all triples on X. In this paper, we give a tripling construction for overlarge sets of KTS. Our main result is that: If there exists an OLKTS(v) with a special property, then there exists an OLKTS(3v). It is obtained that there exists an OLKTS(3(m)(2u 1)) for u = 2(2n-1)-1 or u = q(n), where prime power q 7 (mod 12) and m >= 0, n >= 1.

• 出版日期2009-3-6
• 单位河北师范大学